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# Percentages Study Guide: GED Math

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Updated on Mar 23, 2011

Practice problems for these concepts can be found at:

Percentages Practice Problems:  GED Math

Percentages are just hundredths. In this lesson, you will review how to express given percentages as both fractions and decimals. You'll find that you come into contact with percentages every day with sales tax, tips, and discounts.

### Percents

Percents are everywhere you look. Go to the mall, and you'll see plenty of signs announcing "20% off" or "Take an additional 30% off." Packages at the supermarket regularly claim to include "30% more free." Even your grades for schoolwork are probably percents.

Percent is another way to represent the parts of a whole. Notice that percents are written with the percent sign after a number: 10%, 25%, 30%, 50%, 99%, and so on. The percent sign represents the words out of 100 parts or per 100 parts.

Recall that fractions represent the parts of a whole that is divided into any number of equal parts. So, you can find fractions with any whole number in the denominator: and so on. Decimals represent the parts of a whole that is divided into either 10, 100, 1,000, or another multiple of ten equal parts. Percents, by contrast, always represent a whole that is divided into 100 equal parts. That means that percents can be written as fractions with 100 in the denominator and as decimals written to the hundredths place.

### Converting Percents to Decimals

Changing percents to decimals is as simple as moving the decimal point two digits to the left after removing the percent sign. Follow these basic steps:

Step 1   Drop the percent sign.

Step 2   Add a decimal point if there isn't already one. Remember that even when it's not written in, whole numbers are followed by a decimal point.

Step 3   Move the decimal point two places to the left. Add zeros if needed.

Examples
1. Convert 25% to a decimal.
2. Drop the percent sign (25% becomes 25).

Move the decimal point two places to the left and add a leading zero: 0.25

25% = 0.25

3. Convert 2.5% to a decimal.
4. Drop the percent sign (2.5% becomes 2.5). There is already a decimal point, so move the decimal point two digits to the left. Doing this requires a zero as a placeholder in the tenths place. Also add a leading zero to the left of the decimal point: 0.025.

2.5% = 0.025

### Converting Decimals to Percents

Changing decimals to percents is the opposite of what you've just done. When you change a decimal to a percent, you move the decimal point two digits to the right.

Examples
1. Convert 0.15 to a percent.
2. Move the decimal point two places to the right: 0.15 becomes 15.

Add a percent sign after the number: 15%.

Therefore, 0.15 = 15%.

3. Convert 7.9 to a percent.
4. Move the decimal point two places to the right.

Add zeros as needed: 7.9 becomes 790.

Add a percent sign after the number: 790%.

Therefore, 7.9 = 790%.

### Converting Percents to Fractions

To change a percent to a fraction, you write the percent over 100. Don't forget to reduce the fraction to lowest terms as you would any other fraction. Here are the steps to follow.

Step 1   Drop the percent sign.

Step 2   Write the number as a numerator over 100.

Step 3   Write improper fractions as mixed numbers.

Reduce the fraction to lowest terms.
Examples
1. Convert 15% to a fraction.
2. Drop the percent sign: 15% becomes 15.

Write the number as a numerator over 100: .

Reduce the fraction to lowest terms. Both 15 and 100 can be divided by 5: .

Therefore, 15% = .

3. Convert 150% to a fraction.
4. Drop the percent sign: 150% becomes 150.

Write the number as a numerator over 100: .

Write the improper fraction as a mixed number, and reduce the fraction to lowest terms: .

Therefore, 150% = 1.

### Converting Fractions to Percents

There are two basic ways to convert fractions to percents. You should try both ways, and see which one works better for you.

### Method 1

Step 1   Divide the numerator by the denominator.

Step 2   Multiply by 100. (This is the same as moving the decimal point two digits to the right.)

Step 3   Add a percent sign.

### Method 2

Step 1   Multiply the fraction by .

Step 2   Write the product as either a whole or a mixed number.

Step 3   Add a percent sign.

Example

Change to a percent.

Method 1

Divide the numerator by the denominator.

Multiply by 100: 0.4 × 100 = 40.

Method 2

Multiply the fraction by .

Write the product as either a whole number or a mixed number: 40.

Although you can always convert between percents, decimals, and fractions using the described methods, it's a good idea to know common percent, decimal, and fraction equivalents for standardized tests. Knowing them in advance can save you valuable time on a timed test. Besides, working with a value in one form is often easier than working with it in another form. Knowing the equivalents can help you see the easier route faster. Here are some common equivalents you might want to learn.

Practice problems for these concepts can be found at:

Percentages Practice Problems: GED Math